What's the meaning of the phrase 'Talk to the hand ('cause the face ain't listening)'?

What's the origin of the phrase 'Talk to the hand ('cause the face ain't listening)'?

This appeared, like several other short, mildly intimidating phrases, in the USA in the 1990s. The first reference to it I can find is in this (otherwise unexplained) advertisement in the Wyoming newspaper, The Pinedale Roundup, in Oct, 1996.

It didn't cross the Atlantic right away and the first reference outside the USA is in a piece by Oliver Bennett in The Times, May 1998. In this he recounts a trip to San Francisco and explains some local idioms:

"A contemporary favourite, if you don't like what somebody is saying (a traffic warden, say) is to turn a palm forward and yell: 'Talk to the hand.'"

It seems it wasn't a universal favourite in the USA by then. That same month the Syracuse Herald Journal (New York) reported a vox pop piece that offered the opinion:

"I don't know about you, but if I hear someone say 'talk to the hand' again I will strangle them with their own shoelaces."